One goal of diagnostic medicine is to develop non-invasive tests to replace, or at least precede, invasive tests. For example, one might want to develop a blood test for liver disease, which alternatively can be tested with a liver biopsy. Two critical measures of goodness for a diagnostic test are the sen sitivity of the test, that is, the proportion of truly positive subjects that test positive; and the specificity of the test, the proportion of truly negative subjects that test negative.
Suppose researchers have just discovered a new version of a diagnostic blood test. Data from 100 subjects were collected. Sixty of the subjects were known healthy patients and 40 had liver disease. The test results are given below.
|
|
Test Result Pos Neg
|
|
|
Known Result
|
Pos
|
38
|
2
|
40
|
|
|
Neg
|
8
|
52
|
60
|
|
46
|
54
|
100
|
(a) Estimate the sensitivity and specificity of the test using 95% confidence intervals.
(b) How large a sample of healthy subjects is needed to estimate specificity within 0.05 units with confidence of 95%?
(c) What is the power of this test to detect an increase of 0.03?
(d) A previous version of this diagnostic test had sensitivity 0.90. Using a = 0.05, test to see if the sensitivity of the new improved test is greater.